Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters
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Lesson Description:
Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters -- Lecture 28. Learn about inhomogeneous systems of ODEs by using matrices.
Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 29, 2008). License: Creative Commons BY-NC-SA.
More info at: http://ocw.mit.edu/terms
Additional Resources:
- Lecture Notes - Lecture Notes
- Linear Systems Notes - Linear Systems Notes
- Supplementary Notes - Chapter 24 Supplementary Notes written by Prof. Miller
- Problem Set 7 - Problem Set 7
- Problem Set 7 Solutions - Problem Set 7 Solutions
Questions answered by this video:
- What are Matrix Methods for Inhomogeneous Systems?
- What are Inhomogeneous Systems?
- What is the Fundamental Matrix?
- What is Variation of Parameters?
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Staff Review
An interesting discussion of inhomogeneous systems of linear differential equations by using matrices. The lecture is almost entirely theory, but overall, a good explanation of inhomogeneous systems. Wronskians come up again in this lecture as well, and the fundamental matrix is defined with its properties.
